Momentum dependence of pion-induced $ϕ$ meson production on nuclei near threshold

Abstract

We study the near-threshold pion-induced production of $ϕ$ mesons off nuclei in the kinematical conditions of the HADES experiment, recently performed at GSI. The calculations have been performed within a collision model based on the nuclear spectral function. The model accounts for both the primary $π^-$ meson--proton ${π^-}p \to ϕn$ and the secondary pion--nucleon $πN \to ϕN$ $ϕ$ production processes as well as the effects of the nuclear $ϕ$ and nucleon mean-field potentials. We find that the primary reaction channel ${π^-}p \to ϕn$ dominates in the $ϕ$ production off $^{12}$C and $^{184}$W target nuclei in the HADES acceptance window at incident pion momentum of 1.7 GeV/c. We calculate the momentum dependence of the absolute and relative (transparency ratio) $ϕ$ meson yields from the above direct channel. The calculations have been performed for this initial pion momentum allowing for different options for the $ϕN$ absorption cross section $σ_{ϕN}$ and different scenarios for the in-medium mass shifts of the $ϕ$ meson and secondary neutron, produced together with $ϕ$ in this channel. We demonstrate that the transparency ratio for the $ϕ$ mesons has, contrary to the absolute cross sections, an insignificant sensitivity to the $ϕ$ meson and secondary neutron in-medium mass shifts at $ϕ$ momenta studied in the HADES experiment. On the other hand, we show that there are measurable changes in the transparency ratio due to the $ϕN$ absorption cross section, which means that such relative observable can be useful to help determine this cross section from the data taken in the HADES experiment.